Almost all interesting quantum problems involve degrees of freedom.
Almost invariably in this case
the wavefunction is represented by a
linear sum of basis functions,

(5.4)

This is computationally necessary since it reduces the function
space of to a finite number
of degrees of freedom, namely the coefficient vector .
For a complete basis, any
can be exactly represented by
(5.4) in the limit
.
Clearly a computer can only handle finite , so the basis should be
well chosen so that sufficient convergence is achieved for the
of interest with a manageable .
The choice of basis falls into two general classes:
(A) The basis does not depend on , or
(B) the basis does depend on .
This results in two general strategies, summarized in Table 5.1
and now discussed in detail below.
The nomenclature ``Class A'' etc which I introduce here is new to the literature.